Find the Wronskian of the given pair of functions.
$$
x, x e^{x}
$$
$$
\begin{array}{l}{(x)^{\prime}=1} \\ {\left(x e^{x}\right)^{\prime}=x e^{x}+e^{x}}\end{array}
$$
$$
W=\left|\begin{array}{cc}{x} & {x e^{x}} \\ {1} & {x e^{x}+e^{x}}\end{array}\right|=x^{2} e^{x}+x e^{x}-x e^{x}=x^{2} e^{x}
$$
